You and your friend live 12 miles apart. You leave home at the same time and travel toward each other. You walk at a rate of 4 mph and your friend bicycles at a rate of 11 mph. A) How long after you leave home will you meet? How far from home will each of you be? B) Suppose your friend bikes at a rate of 12 mph. How much sooner will you meet? How far from home will each of you be?
let d be the distance you travel. So 12-d is the distance friend travels. You both pedal for time t (hrs)
d=4t
12-d=11t
add the equations. 12=15t t=12/15 hr
then find d, and 12-d from either equation.
speed toward each other = 11+4 = 15 mph
so time = 12/15 = 4/5 hour = 48 minutes
4/5 * 4 = 16/5 = 3.2 miles
4/5* 11 = 44/5 = 8.8 miles
Now you should be able to do it with a different speed.
A) To find out when you will meet, we need to calculate the time it takes for both of you to cover the total distance of 12 miles.
Let's start with your friend, who is biking at 11 mph. The time it takes for your friend to travel 12 miles can be calculated using the formula:
Time = Distance / Speed
So, for your friend:
Time = 12 miles / 11 mph
Time = 1.09 hours (rounded to the nearest hundredth)
Now, let's calculate your time of travel. You are walking at a speed of 4 mph, so:
Time = 12 miles / 4 mph
Time = 3 hours
Since you both leave home at the same time, we can conclude that you will meet after 1.09 hours (or 1 hour and 5 minutes) after you leave.
To determine how far from home each of you will be, simply multiply the respective speeds by the time traveled.
For your friend:
Distance = Speed × Time
Distance = 11 mph × 1.09 hours
Distance = 11.99 miles (rounded to the nearest hundredth)
For you:
Distance = Speed × Time
Distance = 4 mph × 1.09 hours
Distance = 4.36 miles (rounded to the nearest hundredth)
So, you will meet after 1.09 hours (or 1 hour and 5 minutes) and your friend will be approximately 11.99 miles from home, while you will be approximately 4.36 miles from home.
B) Now let's consider the scenario where your friend is biking at 12 mph instead.
Using the same calculations, we find that the time it takes for your friend to travel 12 miles at a speed of 12 mph is:
Time = 12 miles / 12 mph
Time = 1 hour
For you, walking at 4 mph:
Time = 12 miles / 4 mph
Time = 3 hours
As before, you both leave home at the same time, so you will meet after 1 hour.
To determine how far from home each of you will be:
For your friend:
Distance = Speed × Time
Distance = 12 mph × 1 hour
Distance = 12 miles
For you:
Distance = Speed × Time
Distance = 4 mph × 1 hour
Distance = 4 miles
So, if your friend is biking at 12 mph, you will meet 2 hours earlier than if they were biking at 11 mph. Your friend will be approximately 12 miles from home, while you will be approximately 4 miles from home.
To determine how long it will take for you and your friend to meet, and how far from home each of you will be, we can use the concept of relative speed.
A) When you both travel towards each other, the combined speed is the sum of your walking speed and your friend's bicycling speed, which is 4 mph + 11 mph = 15 mph.
To calculate the time it will take for you to meet, we can divide the distance between you (12 miles) by the combined speed (15 mph):
Time = Distance / Speed
Time = 12 miles / 15 mph
Time = 0.8 hours = 48 minutes
Therefore, approximately 48 minutes after you both leave home, you will meet.
To calculate how far from home each of you will be, we can use the formula:
Distance = Speed × Time.
For you:
Distance = 4 mph × 0.8 hours
Distance = 3.2 miles
You will be approximately 3.2 miles from home.
For your friend:
Distance = 11 mph × 0.8 hours
Distance = 8.8 miles
Your friend will be approximately 8.8 miles from home.
B) Now, let's consider the scenario where your friend bikes at a rate of 12 mph.
The combined speed would then be 4 mph + 12 mph = 16 mph.
Using the same formula as before, we can calculate the time it will take for you to meet:
Time = 12 miles / 16 mph
Time = 0.75 hours = 45 minutes.
Therefore, with your friend biking at 12 mph, you will meet approximately 45 minutes after you both leave home.
To calculate the distance from home for each of you:
For you:
Distance = 4 mph × 0.75 hours
Distance = 3 miles
You will be approximately 3 miles from home.
For your friend:
Distance = 12 mph × 0.75 hours
Distance = 9 miles
Your friend will be approximately 9 miles from home.
So, with your friend biking at 12 mph, you will meet 3 minutes earlier, and you will be 0.2 miles closer to each other.